The rotational and magnetic properties of Polaris from long-term spectropolarimetric monitoring

Abstract: Polaris is a highly unusual Cepheid with observed properties that are difficult to reconcile with stellar evolutionary models. Since the initial detection of Polaris' magnetic field in 2020, we have conducted a magnetic monitoring campaign with the ESPaDOnS spectropolarimeter at the Canada-France-Hawaii Telescope. We compute Stokes $V$ least-squares deconvolution profiles and measure the associated mean longitudinal magnetic field strengths $\langle B_{z}\rangle$. The surface magnetic field has remained remarkably stable over five years of observations, with $\langle B_{z}\rangle$ varying between approximately $-3$ G and $+0.6$ G. From the periodic modulation of $\langle B_{z}\rangle$ we infer a stellar rotation period of $P_{\mathrm{rot}}=100.29\pm0.19$ days. This is the first direct measurement of $P_{\mathrm{rot}}$ for a classical Cepheid. Previous interferometric radius measurements and $P_{\mathrm{rot}}$ imply an equatorial rotation velocity of $v_{\mathrm{eq}}=23.3\pm0.2$ km s$^{-1}$. We set a conservative upper bound on the projected equatorial rotational velocity of $v_{\mathrm{eq}}\sin i_{\star} < 13.5$ km s$^{-1}$ and constrain the stellar inclination angle to be $i_{\star}<37^{\circ}$. Using the previously determined orbital solution, we find a high likelihood of a strong spin-orbit misalignment. We determine the lower bound on the obliquity angle between the stellar rotation and orbital axes to be $β>18.7^{\circ}$ at 99% confidence. We discuss the challenges in interpreting the origin and properties of the surface magnetic field in the context of Polaris' uncertain evolutionary history and the merger hypothesis.